[116.02] Where Are the Asteroids From the Kirkwood Gaps?

Daniel Kirkwood (1888, The Asteroids, Lippincott) proposed
that minor planets whose sidereal periods were commensurate
with Jupiter's period with ratios 1/2, 1/3, etc., had
increasing eccentricity; and at perihelion, collided with
the sun in the early history of the solar system. Jack
Wisdom (1985, Icarus 63, 262) studied the motion of
hypothetical planar asteroids near the 1/3 commensurability,
and concluded that chaotic increases in the eccentricity
would make these asteroids approach Mars and collide or be
strongly deflected from their original orbits. We have made
numerical integrations of accurately observed minor planets
from the 1997 Ephemerides of Minor Planets near the 1/2 and
1/3 Kirkwood gaps. We find that four (1362, 1922, 3688, and
5370) are exactly synchronized, at 1/2 Jupiter's period.
Three (887, 1915, and 6318) are exactly synchronized, at 1/3
Jupiter's period. As seen in a Jupiter-centered coordinate
system, all of these asteroids have libration amplitudes
greater than 30 degrees, but none circulate in integrations
over 1200 Jupiter years. The libration periods vary between
25 and 38 Jyrs. Their Keplerian semi-major axes, listed in
the EMP, differ from the Kirkwood gap values by 0.4 to 2.1
percent. Three of the differences are positive, and four
negative. Answering the title question, at least seven of
them are in orbits about the sun, synchronized to Jupiter,
and listed in the EMP. Our orbit calculations show that they
all have semi-major axes that oscillate about the Kirkwood
values. MP5370 will pass through the Kirkwood gap in about 5
± 0.5 Jyrs, or 59 ± 6 years, from the Dec 18, 1997
epoch used in our calculations.